In: Finance
Suppose you hold a diversified portfolio consisting of a $6,406 invested equally |
in each of 5 different common stocks. The portfolio’s beta is 1.18. Now |
suppose you decided to sell one of your stocks that has a beta of 1 and to |
use the proceeds to buy a replacement stock with a beta of 1.7. What would |
the portfolio’s new beta be? |
1.12
1.02
0.92
1.22
1.32
Your portfolio consists of $80,406 invested in a stock that has a beta = 1.2, |
$97,421 invested in a stock that has a beta = 0.8, and $99,775 invested in a |
stock that has a beta = 1.5. The risk-free rate is 1.8%. Last year this portfolio had |
a required return of 5.7%. This year nothing has changed except that the market |
risk premium has increased by 4.2%. What is the portfolio’s current required rate |
of return? |
10.6%
10.7%
10.9%
10.8%
11.0%
An investor is forming a portfolio by investing $86,534 in stock A that has a beta |
of 2, and $23,817 in stock B that has a beta of 0.4. The market risk |
premium is equal to 2.8% and Treasury bonds have a yield of 2.5%. What is the |
required rate of return on the investor’s portfolio? |
7.33%
7.53%
6.93%
7.13%
6.73%
Assume the risk-free rate is 2% and that the required return on the market is 3.9%. |
If a stock has a required rate of return of 10.5%, what is its beta? |
5.09
4.47
3.57
4.87
3.07
1]
Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.
As it is an equally weighted portfolio, the weight of each stock = 1 / 5 = 0.2
New portfolio beta = old beta - (weighted beta of replaced stock) + (weighted beta of new stock)
New portfolio beta = 1.18 - (0.2 * 1) + (0.2 * 1.7)
New portfolio beta = 1.32
2]
First, we calculate the beta of the portfolio
Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.
weight of each stock = value of stock / value of portfolio
value of portfolio = total of value of stocks = $80,406 + $97,421 + $99,775 = $227,602
Beta of portfolio = (($80,406 / $227,602) * 1.2) + (($97,421 / $227,602) * 0.8) + (($99,775 / $227,602) * 1.5)
Beta of portfolio = 1.16745
Required return = risk free rate + (beta * market risk premium)
Substituting the values for last year into the above equation, we get :
5.87% = 1.8% + (1.16745 * market risk premium)
market risk premium = 3.4862%
New market risk premium this year = 3.4862% + 4.2% = 7.6862%
Required return = risk free rate + (beta * market risk premium)
Required return = 1.8% + (1.16745 * 7.6862%)
Required return = 10.8%
3]
First, we calculate the beta of the portfolio
Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.
weight of each stock = value of stock / value of portfolio
value of portfolio = total of value of stocks = $86,534 + $23,817 = $110,351
Beta of portfolio = (($86,534 / $110,351) * 2) + (($23,817 / $110,351) * 0.4)
Beta of portfolio = 1.16547
Required return = risk free rate + (beta * market risk premium)
Required return = 2.5% + (1.16547 * 2.8%)
Required return = 7.13%
4]
Required return = risk free rate + (beta * (required market return - risk free rate))
10.5% = 2% + (beta * (3.9% - 2%))
beta = (10.5% - 2%) / (3.9% - 2%)
beta = 4.47